Effective chemical potential in spontaneous baryogenesis

TL;DR

This paper challenges the conventional understanding of spontaneous baryogenesis by arguing that the interaction term does not alter single-particle energies, yet baryon asymmetry can still arise from Boltzmann equations, offering a new perspective.

Contribution

The paper demonstrates that the interaction term in spontaneous baryogenesis does not contribute to baryon energies, contrasting with standard assumptions, and explores how baryon asymmetry can still be generated.

Findings

The interaction term does not affect single-particle energies of baryons.

Baryon asymmetry can be derived from Boltzmann equations despite the above.

The arguments differ from standard literature on spontaneous baryogenesis.

Abstract

Models of spontaneous baryogenesis have an interaction term $\partial_\mu\theta j^\mu_B$ in the Lagrangian, where $j^\mu_B$ is the baryonic current and $\theta$ can be a pseudo-Nambu-Goldstone boson. Since the time component of this term, $\dot{\theta} j^0_B$, equals $\dot{\theta} n_B$ for a spatially homogeneous current, it is usually argued that this term implies a splitting in the energy of baryons and antibaryons thereby providing an effective chemical potential for baryon number. In thermal equilibrium, one {then obtains} $n_B \sim \dot{\theta} T^2$. We however argue that a term of this form in the Lagrangian does not contribute to the single particle energies of baryons and antibaryons. We show this for both fermionic and scalar baryons. But, similar to some recent work, we find that despite the above result the baryon number density obtained from a Boltzmann equation analysis can be proportional to $\dot{\theta} T^2$. Our arguments are very different from that in the standard literature on spontaneous baryogenesis.